I apologize for the long post but there is a lot of information here. I bought a pair of Fostex FE207E. Searching for driver break in techniques I found two main ideas, just play music and 20Hz sine wave. I hooked the drivers to an old receiver, one channel was the radio the other was a 20Hz sine wave generated by NCH Tone Generator. Using Unibox, the estimated cone excursion was 0.6mm for the sine wave. The free version of Praxis was used to measure the T/S parameters every hour for the first 10hrs and then every 10hrs for the next 200hrs.
The attached graph of Qts v Time shows a steep drop in Qts from 0 to 4hrs and then a plateau out to 200hrs. There is a peak at 80hrs that I think is anomalous. After 200hrs the radio driver was switched to 20Hz and both drivers increased to an estimated 0.8mm excursion. T/S parameters were measured every 20hrs. Another drop in Qts is seen from 200hrs to 270hrs where another plateau reached out to 370hrs. From 370hrs to 450hrs the drivers were run at an estimated 1.2mm excursion. Little or no change in Qts was found.
If Qts is a fair measure of driver break in then simply playing music at reasonable volume may never break in this driver as shown by the plateau from 4 to 200hrs. Significant driver excursion is clearly required. Exactly how much excursion and for how long would require another experiment.
I hope this is useful.

Qts is only one of the parameters that will change over time. Equally important is Vas. Vas will tend to change in the opposite direction for Qts making the overall tuning of a BR unchanged. Not considered here is that Re will change as the driver warms up, which will cause Qts to lower. So, when you apply more power in your break-in scheme, you must allow the driver to come to the same temperature as your lower power scheme.

IMO, the break-in of a new driver at the bottom end is almost instantaneous. 90% of the break-in can be accomplished by pushing and then pulling the driver to Xsus with you fingers. Unfortunately, most ot the rest of the break-in is reversible and after standing idle for a while, the driver will need to be broken in again for the final 10%.

The top end probably does need some extended break-in, as this involves realigning of the paper fibers. My experience is that you get 90% of this break-in in a couple of hours.

To tell if the sound of a driver changes over time, you will need a number of drivers with different usage levels and then A/B them. It is pure folly to expect of remember how a driver sounded 500 hours ago.

T/S parameters have an important place in the design of speakers, but you have to use them correctly. At the very least:

1. Break in the driver for how ever long you feel moved.

2. Run the driver at the anticipated power level for at least 1/2 hour, which pretty much accomplishes 1 above.

I have found that manually forcing cone suspensions to their mechanical limits changes the driver characteristics similarly to driving them with 'break-in' sines. Such extension was much greater in amplitude and more like X.lim than the calculated X.max, but I have never had the confidence to apply force which causes displacement as high as can be observed by high power LF drive.

I found that driver resonance and mechanical Q became reduced, and thus as Bob mentions the VAS figure was increased.

But here is the curious thing:-

After I did this to one driver of a pair and electrically measured the differences between them, I put both back in their boxes and out of harms way for about two months.
Then when I next opened them and tapped the cones they both sounded the same again !

Before I put them away the tap test difference was obvious, but after a time of rest - not at all !

I found similar findings whether the surronds were treated cloth or roll types, though the degree of change was much less noticable with the treated cloth. Reproduction from the roll surround driver had been notably modified and sounded 'deeper' after stretching, yet after the 'rest' it went back to being 'as new'.

So once a loudspeaker cabinet containing a roll surround driver has been constructed, it is quite literally going to sound different if used gently in one location reproducing classical music compared to another where it gets blasted by pop music bass guitar.

So which driver characteristics should a reflex cabinet be designed for - out of the box, or real-world driven ?

It would be interesting if after you completed your tests you put one back in a box for a couple of weeks and then re-measured.

I only presented Qts results for brevity sake, I've attached Re v Time. Measurements were taken immediately after cycling. Re should increase with temperature. No significant difference is seem in the graph. I believe the reason is that the estimated 1.2mm excursion was reached with only 1.5 volts p-p. Since the drivers impedance is about 18 ohms at 20Hz, the power is only 0.125 w. Not much for the voice coil to dissipate. Re does not explain the change in Qts.
I agree Vas is important but its measurement requires either sticking a weight to the cone or mounting the driver in a box. Since I took over 200 measurements I decided to skip Vas until the end (84l was the result).
I had not considered that the driver could recover from breaking in. Sounds like another experiment.
I have heard the paper fiber alignment argument before but it sets off my bologna detector. Has anyone measured this? It would requre something like X-ray diffraction.